Is Minimize Maximum of Array easy or hard?

Minimize Maximum of Array is classified as Medium difficulty on LeetCode. The implementation is short, but recognizing that the answer depends on prefix averages requires a key greedy insight.

How to solve Minimize Maximum of Array in O(n)?

Compute a running prefix sum while iterating through the array. For each index i, calculate the ceiling average ceil(prefixSum / (i + 1)). Track the maximum of these values across all prefixes. That value represents the smallest possible maximum after redistributing elements left.

What is the best approach for Minimize Maximum of Array?

The prefix sum greedy approach is the most efficient. Track the running prefix sum and compute ceil(prefixSum / prefixLength) at each index. The maximum of these values is the minimized maximum element. This runs in O(n) time and O(1) space.

Is Minimize Maximum of Array asked at Google/Amazon/Meta?

Problems involving greedy redistribution and prefix constraints appear frequently in interviews at companies like Google, Amazon, and Meta. Variants of this question test understanding of prefix sums, greedy reasoning, and binary search on answers.

What data structure is used in Minimize Maximum of Array?

The optimal solution mainly relies on arrays and prefix sums rather than complex data structures. The algorithm maintains a running sum and performs simple arithmetic operations to compute prefix averages.

What is the time complexity of Minimize Maximum of Array?

The optimal greedy solution runs in O(n) time because the array is scanned once while maintaining a prefix sum. Space complexity is O(1). A binary search alternative exists with O(n log m) time where m is the maximum value in the array.

Minimize Maximum of Array Python or Java solution approach?

Most Python and Java implementations follow the same greedy pattern: iterate through the array, maintain a running prefix sum, and compute the ceiling of the average for each prefix. The result is the maximum of those prefix averages, achieved in linear time.

Description Hints 3 Solution Video 9:50

2439. Minimize Maximum of Array

Medium46.4% acceptance5 companies

You are given a 0-indexed array nums comprising of n non-negative integers.

In one operation, you must:

Choose an integer i such that 1 <= i < n and nums[i] > 0.
Decrease nums[i] by 1.
Increase nums[i - 1] by 1.

Return the minimum possible value of the maximum integer of nums after performing any number of operations.

Example 1:

Input: nums = [3,7,1,6]
Output: 5
Explanation:
One set of optimal operations is as follows:
1. Choose i = 1, and nums becomes [4,6,1,6].
2. Choose i = 3, and nums becomes [4,6,2,5].
3. Choose i = 1, and nums becomes [5,5,2,5].
The maximum integer of nums is 5. It can be shown that the maximum number cannot be less than 5.
Therefore, we return 5.

Example 2:

Input: nums = [10,1]
Output: 10
Explanation:
It is optimal to leave nums as is, and since 10 is the maximum value, we return 10.

Constraints:

n == nums.length
2 <= n <= 10⁵
0 <= nums[i] <= 10⁹

Asked at 5 companies

Paytm Visa Microsoft Oracle Amazon

Topics

Hints open one at a time

Hint 1

Try a binary search approach.

Hint 2

Perform a binary search over the minimum value that can be achieved for the maximum number of the array.

Hint 3

In each binary search iteration, iterate through the array backwards, greedily decreasing the current element until it is within the limit.

9:50

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